Potential energy
In 1853, William Rankine introduced the term potential energy during a presentation to the Philosophical Society of Glasgow. The Scottish engineer and physicist sought to create new terminology for the transformation of energy. He chose this specific phrase as part of a pair contrasting actual versus potential states. This choice traced back to ancient Greek philosophy developed by Aristotle. His concept linked directly to the work done against restoring forces like gravity or springs. Rankine later described potential energy in 1867 as energy of configuration. He contrasted it with what he called actual energy or energy of activity. William Thomson would introduce kinetic energy in 1867 as the opposite of potential energy. The phrase actual energy gradually faded from scientific use after that hypothesis gained acceptance.
Forces acting on a body can be classified by how their total work depends on position. If the work done by these forces depends only on initial and final positions, they are conservative forces. A force field varies over space and is described by vectors at every point. Such a field is called a vector field. A conservative vector field expresses itself as the gradient of a scalar function known as a scalar potential. The potential energy relates to and derives from this potential function. The negative sign provides convention where work done against a force field increases potential energy. Work done by the force field decreases potential energy instead. Common notations include PE, U, V, and Ep. The line integral defining work along curve C takes a special form if force F relates to a scalar field U prime x. This means units of U prime must match specific physical dimensions for consistency.
A trebuchet uses gravitational potential energy of a counterweight to throw projectiles over two hundred meters. For small height changes near Earth surface, acceleration due to gravity remains approximately constant. Local gravitational field strength measures 9.8 metres per second squared on Earth. The product of force and displacement gives work done equal to gravitational potential energy. Mass in kilograms multiplied by local gravitational field and height above reference level yields energy in joules. Gravity exerts a constant downward force on center of mass of body moving near Earth surface. Work of gravity on body moving along trajectory calculated using velocity to obtain results. Integral of vertical component of velocity equals vertical distance traveled. Factors affecting object gravitational potential energy include height relative to reference point, its mass, and strength of gravitational field. An object at certain height above Moon surface has less gravitational potential energy than same height above Earth surface because Moon gravity is weaker.
Elastic potential energy arises from deformation under tension or compression within an elastic object. A horizontal spring exerts force proportional to its deformation in axial direction. Contact with spring occurs at zero then integral of product distance x and x-velocity xvx equals half kx squared. Function called potential energy of linear spring describes stored mechanical energy. Elastic potential energy transforms into kinetic energy if stretch released. Electromagnetic force between atoms and molecules constitutes restoring force trying to return object to original shape. Chemical potential energy relates to structural arrangement of atoms or molecules. Fuel burned converts chemical energy to heat during reaction. Green plants transform solar energy to chemical energy through photosynthesis process. Electrical energy converts to chemical energy through electrochemical reactions. Chemical energy of substance transformed to other forms by chemical reaction.
Electrostatic force exerted by charge Q on another charge q separated by distance r follows Coulomb law. Vacuum permittivity epsilon naught defines interaction strength between charges. Work required move q from point A to any point B in electrostatic field given by potential function. Electrically charged particle at rest has potential energy due to position relative to other charged objects. Electrostatic potential energy defined as work done moving it from infinite distance away to present location adjusted for non-electrical forces. Magnetic moment in externally produced magnetic field has potential energy dependent on orientation within field. Needle compass lowest magnetic potential energy when aligned with north and south poles Earth magnetic field. Torque exerts on magnetic dipole needle by Earth magnetic field causing movement back into alignment. Nuclear particles bound together by strong nuclear force inside atomic nucleus. Rest mass provides potential energy for certain kinds radioactive decay like beta decay. Six hundred million tonnes hydrogen nuclei fused into helium nuclei per second in Sun core. Loss about four million tonnes mass per second liberated as heat and radiation in nuclear reactions.
Dinorwig Wales contains two lakes one higher elevation than other used for pumped-storage hydroelectricity. Surplus electricity pumps water up to higher lake converting electrical energy to gravitational potential energy. Water flows back down through generator turbines during peak demand converting potential energy to kinetic energy then electricity. Process not completely efficient some original energy lost to friction. Falling weights operate mechanism powering clocks throughout history. Counterweights lift elevators cranes or sash windows using stored gravitational potential energy. Chains move roller coaster car up incline building gravitational potential energy converted to kinetic energy falling. Automobile truck railroad train bicycle airplane fluid pipeline descend utilizing gravitational potential energy. Commercialization of stored energy rail cars raised higher elevations converts to electrical energy grid system called Advanced Rail Energy Storage ARES undertaken United States. Ski lifts help open twenty-five billion dollar market storing power according to Bloomberg News report September 2012.
Common questions
Who introduced the term potential energy and when?
William Rankine introduced the term potential energy during a presentation to the Philosophical Society of Glasgow in 1853. He sought to create new terminology for the transformation of energy by contrasting actual versus potential states.
What is the relationship between conservative forces and scalar potential functions?
A conservative vector field expresses itself as the gradient of a scalar function known as a scalar potential. The potential energy relates to and derives from this potential function where work done against a force field increases potential energy.
How does gravitational potential energy vary between Earth and the Moon?
An object at certain height above Moon surface has less gravitational potential energy than same height above Earth surface because Moon gravity is weaker. Local gravitational field strength measures 9.8 metres per second squared on Earth while factors include height relative to reference point, its mass, and strength of gravitational field.
What are examples of chemical potential energy transformations?
Green plants transform solar energy to chemical energy through photosynthesis process. Fuel burned converts chemical energy to heat during reaction and electrical energy converts to chemical energy through electrochemical reactions.
How much hydrogen nuclei fuse into helium nuclei per second in Sun core?
Six hundred million tonnes hydrogen nuclei fused into helium nuclei per second in Sun core. Loss about four million tonnes mass per second liberated as heat and radiation in nuclear reactions.